(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 20-kg package is at rest on an incline when a forcePis applied to it. Determine the magnitude ofPif 10s is required for the package to travel 5m up the incline. The static and kinetic coefficients of friction between the package and the incline are both equal to 0.3.

Answer: 419N to start and 301 during sliding

2. Relevant equations

m=20kg

g=9.8m/s^{2}

t=10s

x_{i}= 0ft

x_{f}= 5ft

μ_{s}= μ_{k}= 0.3

Frictional force = F_{f}= μN

3. The attempt at a solution

First, I drew a free-body diagram including tilted coordinate axes:

Then, I went about finding the sum of the forces equations in the x- and y-directions.

[tex]\sum F_{x}=-F_{f}-mgsin(20)+Pcos(30)=ma[/tex]

[tex]\sum F_{y}=N-mgcos(20)-Psin(30)=0[/tex]

From the second equation,

[tex]N=mgcos(20)+Psin(30)[/tex]

Plugging this value for N into F_{f}= μN in the first equation yields:

[tex]P=\frac{m\left(a+\mu gcos(20)+gsin(20)\right)}{cos(30)-\mu sin(30)}[/tex]

If I know the acceleration, I can find the magnitude ofP. There has to be a way to find acceleration from the initial conditions, but I'm at a loss. Also, once static friction is overcome, I'm sure thesum of the forcesequations will be different but I'm not sure how.

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# Homework Help: Determine magnitude of force acting on block on inclined plane

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